Change bone axis orientation
Duplicate one of your bones and rotate 90 degrees on the Z axis. This will be the object from which we will make the desired set of axes.



Open the properties panel using N and press control + alt + spacebar to create a custom axis. In the properties panel under "Transform Orientation" you can rename your custom axis, here I've named it "x = y and y = x".



Now select your original bones, X and Y have traded axes. In the 3D window footer, you can see we are now using the custom orientation created.